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Study on optimization of machining parameters in turning process using evolutionary algorithm with experimental verification
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Study on optimization of machining parameters in turning process using evolutionary algorithm with experimental verification
1. International Journal of Mechanical EngineeringInternational Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN Technology (IJMET), ISSN 0976 – 6340(Print) © IAEMEand 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011),ISSN 0976 – 6359(Online) Volume 2 IJMETNumber 1, Jan - April (2011), pp. 10-21© IAEME, http://www.iaeme.com/ijmet.html ©IAEME STUDY ON OPTIMIZATION OF MACHINING PARAMETERSIN TURNING PROCESS USING EVOLUTIONARY ALGORITHM WITH EXPERIMENTAL VERIFICATION Ganesan.H Department of Mechanical Engineering, RVS College of Engineering & Technology, Coimbatore, Tamilnadu, India. Email: firstname.lastname@example.org Mohankumar.G Park College of Engineering & Technology, Coimbatore, Tamilnadu, India.,.ABSTRACT Optimization of cutting parameters is one of the most important elements in anyprocess planning of metal parts. Economy of machining operation plays a key role incompetitiveness in the market. Turning machines produce finished components fromcylindrical bar. Finished profile from a cylindrical bar is done in two stages, rough machining andfinish machining. Generally more than one passes are required for rough machining andsingle pass is required for finishing. The machining parameters in multipass turning are depthof cut, cutting speed and feed. The machining performance is measured either by theminimum production time or minimum cost. In this paper the optimal machining parameters for continuous profile machiningturning are determined with respect to the minimum production cost, subject to a set ofpractical constraints, cutting force, power, dimensional accuracy and surface finish. Due tocomplexity of this machining optimization problem, genetic algorithm (GA) and particleswarm optimization are applied and results are compared. Key words: Optimization, multipass turning, machining parameters, geneticalgorithm and particle swarm optimization.1. INTRODUCTION It has long been recognized that conditions during cutting, such as feed rate, cuttingspeed and depth of cut should be selected to optimize the economics of machining operations,as assessed by productivity, total manufacturing cost per component or some other suitablecriterion. Agapiou  formulated machining parameter optimization problem consideringboth multi-pass rough machining operations and single-pass finishing. Production cost andtotal time were taken as objectives and a weighting factor was assigned to prioritize the twoobjectives in the objective function. The author optimized the number of passes, depth of cut,cutting speed and feed rate in his model, through a multi-stage solution process calleddynamic programming. Several physical constraints were considered and applied in thismodel. In his solution methodology, every cutting pass is considering as independent of theprevious pass, hence the optimality for each pass is not reached simultaneously. RuyMesquita  used the Hook–Jeeves search method for finding the optimum operatingparameters. Shin and Joo  have presented a model for multipass turning in their research,only the straight turning process, i.e. cutting a component in the longitudinal direction to 11
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEMEproduce a constant part diameter was discussed. The finished component from CNC, in anFMS environment contains a continuous profile. The continuous profile consists of straightturning, facing, taper turning, convex and concave circular arcs. Yellowley et. al  haveshown that for both turning and milling operations the optimal subdivision of depth of cutmay be determined without knowledge of the relevant tool life equation. Calculation ofmachining parameters in turning operation using machining theory was carried out by Mengetet. al . The objective criteria used in this work was minimum cost. Prased et. al [ 6] haveused the combination of geometric and linear programming techniques for solving multi-passturning optimization problem as part of a PC-based generative Computer Aided ProcessPlanning (CAPP) system. Onwubolu et.al had used a genetic algorithm for optimizingmultipass turning operations. Multipass turning optimization with optimal subdivision ofdepth of cut was developed by Gupta et al.  . Saravanan et al.  have developed a new model based on genetic algorithm andsimulated annealing for optimizing machining parameters for turning operation. BhaskaraReddy et al.  have used genetic algorithm to select optimal depth of cut to achieveminimum production cost in multi-pass turning operations. M. C. Chen et al.  havedeveloped an optimization model for a continuous profile using simulated annealingapproach. In this machining model, straight turning, taper turning, and circular turning weresimultaneously considered. James Kennedy et.al.  have developed particle swarmoptimization which is a population-based search procedure that could yield global optimumsolution. K. Choudhri et al.  have also suggested genetic algorithm to find the optimummachining conditions in turning. In this work, two objective functions, namely unitproduction time and unit production cost, were optimized after satisfying few practicalconstraints. Ramon Quiza Sardinas et al.  have also used genetic algorithm for multi-objective optimization problem. The two conflicting objectives are to increase tool life anddecrease operation time. Vijayakumar et al.  have applied ant colony algorithm to findoptimal machining parameters for multi-pass turning operation and also found that theproposed algorithm outperformed the adopted genetic algorithm. Most of the researchers inthe area of machining have used various techniques for finding the optimal machiningparameters for single and multipass turning operations. Traditional techniques are notefficient when the practical search space is too large. Considering the drawbacks of traditionaloptimization techniques, The following table shows the some of the objective functions and constraintsconsidered Year of Sl. Objective Functions Constraint Tool Used Publica No. Considered Considered tions genetic algorithms a) Minimum a) Power (GA) Production time b) Surface finish (2001) 1 b) Minimum c) Cutting force Production cost a) Cutting speed b) Cutting force GA & SA c) power d) Chip tool inter face 2 a) Minimize the cost (2003) e) Dimensional Accuracy f) Surface Finish 12
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME a) Tool life b) Cutting force c) Power a) Minimum Genetic algorithm d) Stable cutting (2005) Production cost 3 region e) Dimensional accuracy a) Depth of cut Genetic algorithm b) Feed rate c) Cutting speed a) Production rate 4 d) Cutting force (2006) b) Tool rate e) Cutting power f) Surface roughness This paper attempts to determine the optimal machining parameters for machining ofa continuous finished profile from bar stock to minimize the production cost using (GA) and(PSO) and the result are compared.2. PROBLEM FORMULATION Turning is a metal cutting process in which job is held and rotated in a chuck, thecutting tool enters and leaves the work piece. The finished component is obtained by anumber of rough passes and a finish pass. The roughing operation is carried out to machinethe part to a size that is slightly larger than the desired size, in preparation for the finishingcut. The finishing cut is called single-pass contour machining, and is machined along theprofile contour, a roughing stages and a finished stage are considered to machine thecomponent from the bar stock. The roughing stage consists of (n-1) passes where n is the totalnumber of roughing passes, and the last pass of roughing removes the material along theprofile contour. In the finish stage material (amount of finish allowance) is removed along thecontour of the profile. The machining time is considered in this work for finding theperformance of the machining operations under practical constraints. The length of cuttingpath is calculated for each pass in the roughing and finishing stages. Then the cutting time foreach pass is calculated for these stages. The objective of this research is to minimize theproduction cost.2.1 Model for Machining PerformanceThe objective of this model is to minimize the production cost which includes machining cost,machine idle cost, the tool replacement cost and the tool cost. The formula for calculating theabove cost is as given by Chen and Su . Finally, by using the above mathematical processes,the unit production cost UC ($/piece) can be obtained asUC=CM + CI + CR + CT =koTM + koT1 + ko(to Tm/tl)+Kt Tm/tewhereCM _ cutting cost ($/piece)CI _ machine idling cost ($/piece)CR _ tool replacement cost ($/piece)CT _ tool cost ($/piece)ko _ sum of direct labour cost and overhead ($/min)TM _ actual cutting timeTI _ machine idle time (min)tl _ tool life (min)te _ time required to exchange a tool (min)kt _ cutting edge cost ($/edge) 13
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME Machining cost can be reduced by optimally selecting the machining parameters. In this workthe equation is considered as objective function and is minimized using optimization. In thisoptimization, following constraints are considered.2.2 Machining Constraints The practical constraints imposed during the roughing and finishing operations asdescribed by Chen and Su are given below.2.2.1 Parameter BoundsBounds on cutting speed: VrL ≤ Vr ≤ VrUwhere VrL and VrU are the lower and upper bounds of cutting speed in roughing, respectively.Bounds on feed: frL < fr < frU where frL and frU are the lower and upper bounds of feed in roughing, respectively.Bounds on depth of cut: drL < dr < drU where drL and drU are the lower and upper bounds of depth of cut respectively. Similarly the above parameter are also considered for finishing.2.2.2 Cutting forceThe cutting force experienced by the work piece during machining will deform the workpiece, try to unclamp the work piece from holding devices and also deflect the tool and toolholder. Hence the cutting force should not exceed certain value(amount) during machining.The expression for the cutting force constraint is given by Fr = kf fr FUwhere Fr is the cutting force during rough machining, kf, and v are the constants pertainingto a specific tool-workpiece combination, and FU is the maximum allowable cutting force(kgf).2.2.3 Power ConstraintThe power available for the spindle is limited, the power constraint is given byPr = ≤ PUwhere Pr is the cutting power during rough machining (kW), η is the power efficiency, and PUis the maximum allowable cutting power (kW).2.2.4 Dimensional Accuracy ConstraintThe accuracy of the machined size not to be compromised beyond certain value. Theregression relation for calculating the dimensional accuracy is given below: δ =100.66.f 0.9709 d0.4905 V-0.2848where δ is the dimensional accuracy, f is the feed rate per revolution, d is the depth of cut,and V is the cutting speed.2.2.5 Surface Finish ConstraintThe certain amount of surface finish is to be maintained for the machined surface after finishcut.The maximum allowable surface roughness is calculated as per equation given by [ ]functional requirement. Surface roughness is influenced by the feed and the nose radius of thetool:where r is the nose radius of cutting tool (mm), Rmax is maximum allowable surface roughness(µ m) and fs is the feed in finish cut. 14
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME3. SOLUTION METHODOLOGY The objective function and its constraints discussed in the previous section are nonlinear and complex. The optimization of machining parameter using conventionaloptimization technique is difficult. Genetic algorithms (GA) and Particle Swarm Optimization(PSO) are best population search based technique.3.1 Genetic Algorithm Methodology Genetic algorithms are computerized search and optimization algorithms based on themechanics of natural genetics and natural selection. Optimization can be done by thegeneration of the population. Genetic algorithms (GA) are a best population search based technique. GA aredifferent from traditional optimizations in the following ways.1. GA goes through solution space starting from a group of points and not from a single point.2. GA search from a population of points and not a single point.3. GA use information of a fitness function, not derivatives or other auxiliary knowledge.4. GA use probabilistic transitions rules, not deterministic rules.5. It is very likely that the expected GA solution will be a global solution. In this paper the cutting conditions are encoded as genes by binary encoding to applyGA in optimization of machining parameters. A set of genes is combined together to formchromosomes, used to perform the basic mechanisms in GA, such as crossover and mutation.. GA optimization methodology is based on machining performance predictions modelsdeveloped from a comprehensive system of theoretical analysis, experimental database andnumerical methods. The GA parameters along with relevant objective functions and set ofmachining performance constraints are imposed on GA optimization methodology to provideoptimum cutting conditions. The following steps are used this methodology1. Choose a coding to represent problem parameters, a selection operator, a crossoveroperator, and a mutation operator. Choose population size n, crossover probability pc, andmutation probability pm. Initialize a random population of strings of size l. Choose amaximum allowable generation number tmax. Set t = 0.2. Evaluate each string in the population.3. If t tmax or other termination criteria are satisfied, terminate.4. Perform reproduction on the population.5. Perform crossover on pair of strings with probability pc.6. Perform mutation on strings with probability pm.7. Evaluate strings in the new population. Set * = t + 1 and go to Step 3.Implementation of GA with Numerical Illustration Implementation is plays an vital role in the genetic algorithm. A problem can besolved once it can be represented in the form of a solution string (chromosomes). The bits(genes) in the chromosome could be binary, real integer numbers. In this work, the cuttingspeed , feed rate and depth of cut are considered to be the primary parameters for the turningoperation. Each of theseprimary variables is represented in a binary string format. The total length of the string is 18in which first 6 bits are used for speed representation and next 6 bits represent the feedvariable and the remaining 6 bits are used as depth of cut parameter. The speed, feed anddepth of cut are represented as substrings in the chromosome. The strings (000000 0000000000000) and (111111 111111 111111) represent the lower and upper limits of speed, feedand depth of cut.Genetic Algorithm ParametersPopulation size: 32Length of Chromosome: 6Selection operator: Rank orderCrossover operator: Single point operatorCrossover probability: 0.75 15
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEMEMutation probability: 0.1Fitness parameter: Operation timeInitialization During initialization, a solution space of a “population size ‘solution string isgenerated randomly between the limits of the speed, feed and depth of cut. In this work thesolution space size (population size) is considered as 18 as shown in Table 1. Columns 1,Column 2 and 3 show the initial random binary population. Column 4 show the objectivefunction output (Optimized output). Here the binary format population can be decoded byusing the below formula.xi = xi(L) + (decoded decimal value)where xi is the decoded speed or feed or depth of cut, x(L) i is the lower limit of speed or feedor depth of cut, x(U) i is the upper limit of speed or feed or depth of cut, and n is the substringlength (= 6).Evaluation In a GA, a fitness function value is computed for each string in the population, andthe objective is to find a string with the maximum fitness function value. It is often necessaryto map the underlying natural objective function to a fitness function form through one ormore mappings. Since, we use a minimization objective function, the followingtransformation is usedf(x) =where g(x) is the objective function (Operation time) and f(x) is the fitness function. In theminimization problem the string which has the higher fitness value will be the best string.Selection and Reproduction Reproduction selects good strings in a population and forms a mating pool. Thereproduction operator is also called a selection operator. In this work rank order selection isused. In Table 1 Column 4 shows the output generated using this method. Column 5 is thecorresponding rank of the string. A lower ranked string will have a lower fitness value or ahigher objective function and vice versa. The higher cumulative probability value in the range is chosen as one of the parents. InTable 1 for the first string the generated random number is 0.237122. The string number(rank) 1, which has a cumulative probability of 0.2485000, is selected as the parent, and thisprocess is repeated for the entire population.Crossover Crossover is a mechanism for diversification. The strings to be crossed and thecrossing points are selected randomly and crossover is done with a crossover probability. Asingle-point crossover is used in this work. The crossover probability is 0.75. The concept ofcrossover is explained below.Before crossover:1. 110010 – 00 | 01112. 110100 – 01 | 0010After crossover: 1&2→9 means crossover takes place between 1st and 2nd string at (9 + 1)thcross site and after the (9 + 1)th bit all the information is exchanged between strings. Thecross site number starts from zero. Hence cross site number 9 represents the 10th site.1. 110010 – 01 | 01112. 110100 – 00 | 0010Mutation Mutation is a random modification of a randomly selected string. Mutation is donewith a mutation probability of 0.1.Before mutation:1. 11001001_0_111 16
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEMEAfter mutation: 1→9 means that mutation takes place at the 1st string at the 9th site. Themutation will invert from 0 to 1 or 1 to 0 at the particular site.1. 11001001_1_111The output after the first iteration is given in Table 2. The best string in the list is thechromosome rank 1 which has minimum unit production cost. This completes one iterationof the GA and the best value is stored. All the strings available at the end of first iteration willbe treated as parents for the second iteration. This procedure is repeated for the number ofiterations as given by the user.In this example,x i (L) = 50 for speed x i (U) = 3500 for speed (L)x i = 0.01for feed x i (U) = 0.4 for feed (L)x i =0.3 for depth of cut x i (U) = 1.5 for depth of cutTable 1 Unit speed feed dept cut Cost 104.762 0.171 1.424 3.7 104.762 0.4 1.481 2.33 269.048 0.171 1.424 2.251 323.81 0.362 1.405 1.779 323.81 0.4 1.5 1.751 1966.667 0.133 1.462 1.622 1802.381 0.171 1.5 1.603 1857.143 0.167 1.5 1.603 1857.143 0.171 1.348 1.6 1857.143 0.171 1.5 1.6 2514.286 0.148 1.5 1.586 2295.238 0.171 0.795 1.582 2514.286 0.171 0.814 1.574 1857.143 0.248 1.386 1.569 1857.143 0.248 1.329 1.569 1857.143 0.319 1.176 1.554 2459.524 0.324 1.252 1.54 2733.333 0.324 1.481 1.536Table 2 Unit speed feed dept cut Cost 2733.333 0.324 1.481 1.536OutputFigure 1 17
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME3.2 Particle Swarm Optimization (PSO)In this proposed algorithm we are using single-objective PSO to optimization problems.PSO Algorithm1. For i = 1 to M (M is the population size) a. Initialize P[i] randomly (P is the population of particles) b. Initialize V[i] = 0 (V is the speed of each particle) c. Evaluate P[i] d. Initialize the personal best of each particle PBESTS[i] = P[i] e. GBEST = Best particle found in P[i]2. End For3. Initialize the iteration counter t = 04. Store the vectors found in P into A (A is the external archive that stores solutions found in P)5. Repeat a. Compute the crowding distance values of each solution in the archive A b. Sort the solutions in A in descending crowding distance values c. For i = 1 to M i. Randomly select the global best guide for P[i] from a specified top portion (e.g. top 10%) of the sorted archive A and store its position to GBEST. ii. Compute the new velocity: V[i] = W x V[i] + R1 x (PBESTS[i] – P[i]) + R2 x (A[GBEST] – P[i]) (W is the inertia weight equal to 0.4) (R1 and R2 are random numbers in the range [0..1]) (PBESTS[i] is the best position that the particle i have reached) (A[GBEST] is the global best guide for each solution) iii. Calculate the new position of P[i]: P[i] = P[i] + V[i] iv. If P[i] goes beyond the boundaries, then it is reintegrated by having the decision variable take the value of its corresponding lower or upper boundary and its velocity is multiplied by -1 so that it searches in the opposite direction. v. If (t < (MAXT * PMUT), then perform mutation on P[i]. (MAXT is the maximum number of iterations) (PMUT is the probability of mutation) vi. Evaluate P[i] d. End For e. Insert all new solution in P into A if they are not dominated by any of the stored solutions. All dominated solutions in the archive by the new solution are removed from the archive. If the archive is full, the solution to be replaced is determined by the following steps: i. Compute the crowding distance values of each solution in the archive A ii. Sort the solutions in A in descending crowding distance values iii. Randomly select a particle from a specified bottom portion (e.g. lower 10%) which 258 comprise the particles in the archive then replace it with the new solution f. Update best solution of each particle in P. If the current PBESTS dominates the position in memory, the particles position is updated using PBESTS[i] = P[i] g. Increment iteration counter t6. Until maximum number of iterations is reached 18
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME Generate initial population Evaluate initial particles to get Update velocities for all the particles Update particle position Evaluate the updated particle to get No Stop criteria met? Yes Print the Gbest particle End Figure 2: The algorithm for Particle Swarm OptimizationGlobal Best SelectionThe selection of the global best guide of the particle swarm is a crucial step in a PSOalgorithm. It affects both the convergence capability of the algorithm as well as maintaining agood spread of solutions. We want to ensure that the particles in the population move towardsthe sparse regions of the search space. In PSO the global best guide of the particles is selectedfrom among those solutions with the best values.MutationThe mutation operator of PSO was adapted because of the exploratory capability it could giveto the algorithm by initially performing mutation on the entire population then rapidlydecreasing its coverage over time. This is helpful in terms of preventing prematureconvergence due to existing local Pareto fronts in some optimization problems.Constraint HandlingIn order to handle constrained optimization problem PSO due to its simplicity in usingfeasibility and the solutions when comparing final output. A solution is said to constrained-dominate a solution j if any of the following conditions is true: 19
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME1. Solution i is feasible and solution j is not.2. Both solutions i and j are infeasible, but solution i has a smaller overall constraint violation.3. Both solutions i and j are feasible and solution i dominates solutions j.When comparing two feasible particles, the particle which dominates the other particle isconsidered a better solution. On the other hand, if both particles are infeasible, the particlewith a lesser number of constraint violations is a better solution.The Time Complexity of PSOThe computational complexity of the algorithm is dominated by the objective functionOperation time and Unit of Cost in the archive. If there are M objective functions and Nnumber of solutions (particles) in the population, then the objective function computation hasO(MN) computational complexity. If there are K solutions in the archive, sorting the solutionsin the archive has O(M K log K) computational complexity.Output:Table 3 Unit speed feed dept cut Cost 2650 0.41 1.32 1.4024. TEST EXAMPLEFor testing the proposed methodology, the component shown in Fig.3 is considered. Thecomponent is to be machined with optimal speed and feed using an SUPER JOBBER LMCNC turning centre in an industry. The work piece material is EN 8 and the tool material is acarbide tip. The proposed model is run on an FANUC OI TD computer using the C++language. Tables and graphs summaries the computational results.Number of roughing cuts - 11Depth of cut for finishing - 0.3 mm Figure 3. Test Component5. RESULTS AND DISCUSSIONThe GA optimization is done for 500 iterations. The results obtained from GA optimizationare given in Table 1. The optimal cutting parameters such as speed, feed and depth of cutobtained from GA for the minimum cost of 1.536. Figure 2 shows the fitness obtained in eachiteration of the GA. The graph shows that the GA produces smooth fitness at the initialiteration and varying fitness in the subsequent iterations. The GA and PSO Optimization iscoded in C++ language. The optimal cutting parameters such as speed, feed and depth of cutand constraints are considered in PSO and the result obtained with the minimum cost of 1.402shown in Table 3 20
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),ISSN 0976 – 6359(Online) Volume 2, Number 1, Jan - April (2011), © IAEME6. CONCLUSIONAll types of CNC machines have been used to produce continuous finished profiles. Acontinuous finished profile has many types of operations such as facing, taper turning andcircular turning. To model the machining process, several important operational constraintshave been considered. These constraints were taken to account in order to make the modelmore realistic. A model of the process has been formulated with non-traditional algorithms;GA and PSO have been employed to find the optimal machining parameters for thecontinuous profile. PSO produces better results. Using this technique production cost can befurther minimized. The results show that the production cost is minimized by using theoptimized machining parameter.REFERENCES1. Agapiou,( 1992) “The optimization of machining operations based on a combined criterion,Part-1: the use of combined objectives in single pass operations”, ASME Journal ofEngineering for Industry, 114, pp. 500–507,.2. Ruy Mesquita et al.(1995), “Computer aided selection of optimum machining parameters inmulti pass turning”, International Journal of Advanced Manufacturing technology, 10, pp. 19–263.Y. C. Shin, Y. S. Joo, (1992)"Optimization of machining conditions with practicalconstraints", Int. J. Prod. Res., vol. 30, no. 12, pp. 2907–2919,.4. I. Yellowley et al.( 1992), “The optimal subdivision of cut in multi pass machiningoperation”, International Journal of Material Processing Technology, 27, pp. 1572–1578,.5.Q. Meng et al. (2000), “Calculation of optimum cutting condition for turning operationusing a machining theory”, International Journal of Machine Tool and Manufacture, 40,pp.1709–1733,.6 A. V. S. R. K. Prasad et al.( 1997), “Optimal selection of process parameters for turningoperations in a CAPP system”, International Journal of Production Research, 35, pp.1495–1522,.7. G. C. Onwubolu et al. (2001), “Multi-pass turning operations optimisation based on geneticalgorithms”, Proceedings of Institution of Mechanical Engineers, 215, pp. 117–124,8. R. Gupta et al.,(1995) “Determination of optimal subdivision of depth of cut in multi-passturning with constraints”, International Journal of Production Research, 33(9), pp.2555–2565,9.R. Saravanan et.al (2003)Machining Parameters “Optimisation for Turning CylindricalStock into a Continuous Finished Profile Using Genetic Algorithm (GA) and SimulatedAnnealing (SA)” Int J Adv Manuf Technol 21:1–9,10. Bhaskara Reddy SV, Shunmugam MS, Narendran TT (1998) Optimal subdivision of thedepth of cut to achieve minimum production cost in multi-pass turning using a geneticalgorithm. J Mater Process Technol 79:101–108,11.M. C. Chen and C. T. Su,(1998) “Optimization of machining conditions for turningcylindrical stocks into continuous finished profiles”, International Journal of ProductionResearch, 36(8), pp. 2115–2130,12. James Kennedy and Russell Eberhart (2000)"Particle swarm optimization", Proceeding ofIEEE International Conference on Neural Networks, IV, pp. 1,942–1,948.13. Choudhri K, Prathinar DK, Pal DK, (2002) Multi objective optimization in turning—using a genetic algorithm. J Inst Eng 82:37–44,14.Ramon Quiza Sardinas, Santana MR, Brindis EA (2006) “Genetic algorithm-based multi-objective optimization of cutting parameters in turning processes” Published in EngineeringApplications of Artificial Intelligence 19 127 – 13315. Vijayakumar K, Prabhaharan G, Asokan P, Saravanan R (2003) Optimization of multi-pass turning operations using ant colony system. Int J Mach Tools Manuf 43:1633–1639,16.Kalyanmoy Deb, (1996). “Optimizations for engineering design – Algorithm andexamples”, Prentice-Hall of India, New Delhi 21
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